Subtract $-2x^2+4x-1$ from $6x^2+3x-9$.
Explanation: Since we are asked to subtract $-2x^2+4x-1$ from $6x^2+3x-9$, let's rewrite it as one expression. But how do we know which terms go where? Well, if we were asked to "subtract $3$ from $10$ ", we would rewrite it as $10 - 3$. In other words, we would start with $10$ and then subtract $3$. Let's use this pattern to rewrite the problem as one expression: ${(6x^2+3x-9)-(-2x^2+4x-1)}$ Since we are subtracting, it is helpful to distribute the $\text{{negative sign}}$ across all terms in the second trinomial: $\begin{aligned}&(6x^2+3x-9){-}(-2x^2+4x-1)\\ \\ =&(6x^2+3x-9){-}(-2x^2){-}4x{-}(-1)\\ \\ =&6x^2+3x-9+2x^2-4x+1 \end{aligned}$ Note that the parentheses around the first trinomial don't affect the order of operations, so we can just remove them. When we add or subtract terms in a polynomial expression, the only way that we can simplify the expression is by combining those terms that are alike. Our expression contains terms of $3$ different degrees in the same variable: ${x^2}, {x},$ and the $\text{{constant}}$ term: ${{6x^2} {+3x} {-9} {+2x^2} {-4x} {+1}}$ Now that we have identified like terms, let's combine them. Make sure to keep track of positive and negative signs! ${{(6+2)x^2} + {(3-4)x} + {(-9+1)}}$ When we combine the coefficients in front of each term, we get the following trinomial: ${8x^2 -x -8}$